1. Field of the Invention
The invention pertains to the field of pulse Doppler radar systems and more particularly to the elimination of range and Doppler ambiguities in such radar systems.
2. Description of the Prior Art
A pulse Doppler radar system suffers a serious performance deficiency, referred to as the pulse Doppler dilemma, which stems from the relationship between the pulse repetition rate and the measurable unambiguous range and Doppler frequency. This deficiency constrains the data quality of weather parameter measurements obtained with pulse Doppler radar systems.
As is well known, a pulse radar system determines the range to a target, which for a weather radar system is the atmospheric volume, by measuring the elapsed time between the transmission or a radar pulse and the subsequent reception of the target's backscatter of that pulse, the elapsed time being t=(2R)/C, where R is the range to the target and C is the velocity of light. Since the receiver can not distinguish between a return from a target of the most recent transmitted pulse and a return from another target of an earlier transmitted pulse, the maximum unambiguous time available for unambiguous receiver reception is the time between successive pulse transmissions. Thus, the maximum unambiguous range is R.sub.max =(CT)/2, T being the interpulse transmission interval. As is also well known, a pulse Doppler radar system determines the relative velocity of a target by measuring the Doppler shift of a spectral line of the radiation frequency spectrum of the received backscattered pulse train. The spectral lines in such systems are established by the transmission of a train of pulses at a given repetition rate. The frequency spacing between these spectral lines is equal to the repetition rate of the pulse train, which is equal to (1/T). When a target (backscatter) is moving in a direction which causes the radial distance between the target and the transmitter to decrease (closing target), the spectral line frequency increases by f.sub.DC =(2v.sub.C)/.lambda., .lambda. being the wavelength of the radiated wave. Conversely, when the target is moving in a direction which causes the radial distance between the target and the transmitter to increase (opening target), the spectral line frequency decreases by f.sub.DO =(2v.sub.o)/.lambda.. In such pulse doppler radar systems the n.sup.th spectral line is chosen as a reference and the Doppler frequency shift of this spectral line in the frequency bands between it and the two adjacent spectral lines, n-1 and n+1, is measured to obtain the velocity of the target. As will subsequently be more fully explained, the 1/T spacing of the spectral lines limit the unambiguous measurement of the Doppler shifted spectral line f.sub.n to the band f.sub.n .+-.1/(2/T). Consequently, the maximum unambiguous velocity, V.sub.max, that can be measured is EQU V.sub.max =.+-..lambda./(4T)
This result may also be obtained with the application of the well known sampling theorem, which states that a coherently detected radar signal must be measured at sample time spacings that are no greater than 1/(2f.sub.D) to unambiguously measure f.sub.D. If f.sub.D is the maximum unambiguous detectable Doppler frequency, it follows that the maximum unambiguous measurable target velocity, V.sub.max, that can be measured for an interpulse interval, T=1/f.sub.D, is V.sub.max =.+-..lambda./(4T).
Thus it is apparent that the maximum unambiguous range that can be measured with a pulse doppler radar system increases with increasing interpulse intervals, while the maximum unambiguous velocity that can be measured decreases with increasing interpulse intervals. In many instances the unambiguous velocities to be measured by a pulse doppler radar system require interpulse intervals that are too short to provide the desired maximum unambiguous range measurement.
Multiplying the maximum range expression R.sub.max by the maximum velocity expression V.sub.max yields the well known "pulse Doppler dilemma" EQU R.sub.max V.sub.max =(C.lambda.)/8
This dilemma is illustrated in FIG. 1 for a pulse doppler radar operating at 3 GHz.
Since the range to a target is determined by the elapsed time between the transmission of a pulse and the reception of its echo, echoes of previously transmitted pulses returned from targets at ranges beyond C/(2T) appear at range positions in the range interval of the last transmitted pulse. This condition is known as "range folding" and is illustrated in FIGS. 2 and 3.
A pulse train having an interpulse interval of sufficient length to permit radar returns of a transmitted pulse from targets at all ranges of interest before the transmission of the succeeding pulse is shown in FIG. 2. As shown in the figure, target returns R.sub.S11, R.sub.S12, and R.sub.S13, of the transmitted pulse T.sub.S1, from targets at three different ranges are received prior to the transmission of the succeeding pulse T.sub.S2. Similarly, returns R.sub.S21, R.sub.S22, and R.sub.S23 and R.sub.S31, R.sub.S32, and R.sub.S33 of pulse transmission T.sup.S1 and T.sub.S2, respectively, from the same three different ranges are also received prior the transmission of the succeeding pulse. Thus the range to the three targets may be unambiguously determined.
When the pulse repetition rate is increased, as shown in FIG. 3, the ranges to the targets at the same three different ranges cannot be determined unambiguously. Shown in the figure are signal returns (R.sub.Fn1, R.sub.Fn2, R.sub.Fn3 ; n=1,2,3,4) from targets at the same three different ranges resulting from transmissions of pulses T.sub.Fn at the higher pulse repetition rate. After the transmission of T.sub.F1, a signal return is received from the target at the first range (R.sub.F11) prior to the transmission of the second pulse T.sub.F2. The signal returns R.sub.F12 and R.sub.F13 are not, however, received before the transmission of the pulse T.sub.F2. The signal return R.sub.F12 is received in the interval between the transmission of pulses T.sub.F2 and T.sub.F3, while the signal return R.sub.F13 is received in the interval between the transmission of pulses T.sub.F3 and T.sub.F4. Similarly, the signal return R.sub.F21 is received in the interval between the transmissions of pulses T.sub.F2 and T.sub.F3, while the signal return R.sub.F22 is received in the interval between the pulse transmissions T.sub.F3 and T.sub.F4, while the signal return R.sub.F23 is received in the interval between the pulse transmissions T.sub.F4 and T.sub.F5. Thus, two returned signals are received in the interval between pulse transmissions T.sub.F2 and T.sub.F3 and three in the interval between T.sub.F3 and T.sub.F4 and all other interpulse intervals. Though the returns from the three targets appear in the interpulse interval between T.sub.F3 and T.sub.F4, and all succeeding interpulse intervals, only one return is due to the transmission of the pulse initiating the interval and only one unambiguous range is measured. For example, the elapsed time between the transmission of the pulse T.sub.F3 and the reception of the signal R.sub.F31 provides the correct range to the target from which the pulse was reflected, while the measured elapsed time between the transmission of T.sub.F3 and the reception of the signals R.sub.F13 and R.sub.F22, which are not reflections of the transmitted pulse T.sub.F3, provide ranges that are ambiguous.
Illustrations of Doppler frequency shifts of spectral lines are shown in FIGS. 4A through 4C. Three spectral lines, f.sub.n-1, f.sub.n, and f.sub.n+1 (f.sub.n+1 =f.sub.n +1/T; f.sub.n-1 =f.sub.n -1/T) are shown in the figures, f.sub.n being the reference. Doppler shifted frequencies of f.sub.n caused by closing targets with velocities v.ltoreq..lambda./4T are in the frequency band between f.sub.n +1/(2T) and f.sub.n, while Doppler shifted frequencies of f.sub.n caused by opening targets, in the same velocity range, are in the band between f.sub.n and f.sub.n -1/(2T). FIG. 4A illustrates the Doppler frequency shift, .DELTA.f.sub.C, of the three spectral lines due to a target decreasing the radial distance at a velocity that is less than .lambda./(2T) and the Doppler frequency shift, .DELTA.f.sub.o, of the three spectral lines caused by a target that is increasing the radial distance at a velocity that is also less than .lambda./(2T). The Doppler shifted spectral lines, (.sub.fn-1 +.DELTA.f.sub.C) and (f.sub.n+1 +.DELTA.f.sub.C), caused by the closing target and the Doppler shifted spectral lines, f.sub.n-1 -.DELTA.f.sub.o and f.sub.n+1 -.DELTA.f.sub.o, caused by the opening target do not penetrate the frequency band f.sub.n .+-.1/(2T) and the measurement of the Doppler frequency shift is unambiguous.
FIG. 4B illustrates the Doppler shifted spectral lines caused by a target moving radially toward the radar location at a velocity that is greater than .lambda./(4T). In this situation the spectral line f.sub.n is Doppler shifted up to a frequency f.sub.n +.DELTA.f.sub.C that is out of the frequency band f.sub.n .+-.1(2T), while the spectral line f.sub.n-1 is Doppler shifted into the frequency band f.sub.n .+-.1(2T).
Since the frequency measurements are restricted to the band f.sub.n .+-.1(2T), the Doppler frequency shift, f.sub.DC, that is measured is -[1/T-.DELTA.f.sub.C ], which translates to an erroneous radial range opening velocity indication equal to [-.lambda.(1T-.DELTA.f.sub.C)/2] rather than the true closing velocity .lambda..DELTA.f.sub.C /2. It should be recognized that closing velocities are considered positive velocities and opening velocities are considered negative.
FIG. 4C illustrates the Doppler shifted spectral lines caused by a target moving radially away from the radar location at a velocity that is greater than .lambda./(2T). Under these conditions the spectral line f.sub.n is Doppler shifted down to a frequency f.sub.n -.DELTA.f.sub.o, a frequency that is out of the frequency band f.sub.n .+-.1/(2T), while the +spectral line f.sub.n-1 is down shifted to a frequency f.sub.n+1 -.DELTA.f.sub.o which is in the frequency band f.sub.n .+-..DELTA.f.sub.o. Consequently, the measurement of the Doppler shift of the spectral line f.sub.n within the frequency band .+-.1/(2T) provides a Doppler frequency, f.sub.DO, equal to 1/T-.DELTA.f.sub.o rather than the true Doppler frequency shift .DELTA.f.sub.o. The ambiguous Doppler frequency shift represents a velocity equal to .lambda.(1/T-.DELTA.f.sub.o)/2 rather than the true velocity (-.lambda.f.sub.o /2).
Doppler frequency is determined from the phase shift of the transmitted signal caused by the movement of the backscattering target. Phase is a function of frequency and time and is expressed at .PHI.=2.pi.ft. Therefore, the phase shift caused by the movement of the target in the interpulse period of FIG. 4B is .sub.DA =2.pi.(f.sub.n +f.sub.DA)T. The phase determined from the apparent Doppler shift f.sub.DC is .PHI..sub.M =2.pi.(f.sub.n -(1/T)+f.sub.DA)T=2.pi.(f.sub.n +f.sub.DA)T=2.pi.(f.sub.n +f.sub.DA)-2.pi.. Thus, the actual phase of the signal at the Doppler shifted frequency is related to the measured phase by .PHI..sub.DA =.PHI..sub.M +2.pi.. In FIG. 4A it has been assumed that the movement of the target has shifted the spectral lines by a frequency that is less than 1/T so that the Doppler shifted spectral line f.sub.n-1 does not appear in the .+-.1/(2T) measurement band about f.sub.n. The target velocity, however, may be such as to cause the Doppler shifted spectral line f.sub.n-k to appear in the measurement band. Consequently, the general expression for the phase ambiguity is EQU .PHI..sub.DA =.PHI..sub.M +2k.pi.
It should be apparent that, unless the target velocities are known to cause Doppler shifts of the spectral lines that remain within the band f.sub.n .+-.1/(2T), the phase determination provided by a pulse doppler radar is multiply ambiguous.
To resolve the range and velocity ambiguities, a weather radar of the prior art employs a relatively long interpulse interval, T.sub.R, for measuring precipitation reflectivity and a shorter interpulse interval, T.sub.V, for measuring radial velocity. To place velocity and spectrum information at the correct range location this prior art system employs a range-unfolding algorithm which compares the amplitude of all the received echoes within the range interval C/(2T.sub.V) of the latest transmitted pulse and selects the one echo amplitude that exceeds a predetermined threshold as the return due to the latest pulse transmission. If none of the echoes exceed this threshold the echo information is not utilized. Consequently, important meteorological velocity information may be discarded because the range to the meteorological scatters can not be determined unambiguously.